14a-18a^3-26a^5=

Solution for 14a-18a^3-26a^5= equation:

Simplifying
14a + -18a3 + -26a5 = 0

Solving
14a + -18a3 + -26a5 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2a'.
2a(7 + -9a2 + -13a4) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

Move all terms containing a to the left, all other terms to the right.

Simplifying
a = 0
Subproblem 2
Set the factor '(7 + -9a2 + -13a4)' equal to zero and attempt to solve:

Simplifying
7 + -9a2 + -13a4 = 0

Solving
7 + -9a2 + -13a4 = 0

Begin completing the square.  Divide all terms by
-13 the coefficient of the squared term: 

Divide each side by '-13'.
-0.5384615385 + 0.6923076923a2 + a4 = 0

Move the constant term to the right:

Add '0.5384615385' to each side of the equation.
-0.5384615385 + 0.6923076923a2 + 0.5384615385 + a4 = 0 + 0.5384615385

Reorder the terms:
-0.5384615385 + 0.5384615385 + 0.6923076923a2 + a4 = 0 + 0.5384615385

Combine like terms: -0.5384615385 + 0.5384615385 = 0.0000000000
0.0000000000 + 0.6923076923a2 + a4 = 0 + 0.5384615385
0.6923076923a2 + a4 = 0 + 0.5384615385

Combine like terms: 0 + 0.5384615385 = 0.5384615385
0.6923076923a2 + a4 = 0.5384615385

The a term is 0.6923076923a2.  Take half its coefficient (0.3461538462).
Square it (0.1198224852) and add it to both sides.

Add '0.1198224852' to each side of the equation.
0.6923076923a2 + 0.1198224852 + a4 = 0.5384615385 + 0.1198224852

Reorder the terms:
0.1198224852 + 0.6923076923a2 + a4 = 0.5384615385 + 0.1198224852

Combine like terms: 0.5384615385 + 0.1198224852 = 0.6582840237
0.1198224852 + 0.6923076923a2 + a4 = 0.6582840237

Factor a perfect square on the left side:
(a2 + 0.3461538462)(a2 + 0.3461538462) = 0.6582840237

Calculate the square root of the right side: 0.811347043

Break this problem into two subproblems by setting 
(a2 + 0.3461538462) equal to 0.811347043 and -0.811347043.

Subproblem 1
a2 + 0.3461538462 = 0.811347043

Simplifying
a2 + 0.3461538462 = 0.811347043

Reorder the terms:
0.3461538462 + a2 = 0.811347043

Solving
0.3461538462 + a2 = 0.811347043

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-0.3461538462' to each side of the equation.
0.3461538462 + -0.3461538462 + a2 = 0.811347043 + -0.3461538462

Combine like terms: 0.3461538462 + -0.3461538462 = 0.0000000000
0.0000000000 + a2 = 0.811347043 + -0.3461538462
a2 = 0.811347043 + -0.3461538462

Combine like terms: 0.811347043 + -0.3461538462 = 0.4651931968
a2 = 0.4651931968

Simplifying
a2 = 0.4651931968

Take the square root of each side:
a = {-0.682050729, 0.682050729}

Subproblem 2
a2 + 0.3461538462 = -0.811347043

Simplifying
a2 + 0.3461538462 = -0.811347043

Reorder the terms:
0.3461538462 + a2 = -0.811347043

Solving
0.3461538462 + a2 = -0.811347043

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-0.3461538462' to each side of the equation.
0.3461538462 + -0.3461538462 + a2 = -0.811347043 + -0.3461538462

Combine like terms: 0.3461538462 + -0.3461538462 = 0.0000000000
0.0000000000 + a2 = -0.811347043 + -0.3461538462
a2 = -0.811347043 + -0.3461538462

Combine like terms: -0.811347043 + -0.3461538462 = -1.1575008892
a2 = -1.1575008892

Simplifying
a2 = -1.1575008892

Reorder the terms:
1.1575008892 + a2 = -1.1575008892 + 1.1575008892

Combine like terms: -1.1575008892 + 1.1575008892 = 0.0000000000
1.1575008892 + a2 = 0.0000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
a = {0}